Cancellation in semigroups in which X²=X³

1. Brown, T. C.,A semigroup union of disjoint locally finite subsemigroups which is not locally finite, Pacific J. of Math. 22 (1967), 11–14.

   MATH  Google Scholar 

2. Brzozowski, J. A., K. Culik II, and A. Gabrielian,Classification of noncounting events, J. Comput. Syst. Sci. 5 (1971), 243–271.

   MathSciNet  Google Scholar 

3. Dean, R.,A sequence without repeats on x, x⁻¹, y, y⁻¹, Am. Math. Mon. 72 (1965), 383–385.

   Article  MATH  MathSciNet  Google Scholar 

4. Dejean, F.,Sur un théorème de Thue, J. Comb. Theory A13 (1972), 90–99.

   Article  MATH  MathSciNet  Google Scholar 

5. Gerhard, J. A.,The word problem for semigroups satisfying x³=x, Math. Proc. Camb. Phil. Soc. 84 (1978), 11–19.

   Article  MATH  MathSciNet  Google Scholar 

6. Green, J. A., and D. Rees,On semigroups in which x^r=x, Proc. Camb. Philos. Soc. 48 (1952), 35–40.

   MATH  MathSciNet  Google Scholar 

7. Lallement, G.,Semigroups and Combinatorial Applications, Wiley-Interscience, New York, 1979.

   MATH  Google Scholar 

8. Leech, L.,A problem on strings of beads, Math. Gaz. 41 (1957), 277–278.

   Article  MATH  MathSciNet  Google Scholar 

9. Morse, M., and G. A. Hedlund,Unending chess, symbolic dynamics and a problem in semigroups, Duke Math. J. 11 (1944), 1–7.

   Article  MATH  MathSciNet  Google Scholar 

10. Shevrin, L. N., personal communication, 1967.

11. Thue, A.,Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen, Skr. Vid. Kristiania, I Mat. Naturv. Klasse 8 (1912), 1–67.

    Google Scholar 

Download references